Concyclicity of points — task. Maths CBSE Live product, Class 9 (2026-27).

Consider the segment \(AB\) of the circle. The points \(C\) and \(D\) lie on the same side of \(AB\). If \(\angle ACB = 43^{\circ}\) and \(\angle ADB = 43^{\circ}\), then say whether the points \(A\), \(B\), \(C\) and \(D\) are concyclic or not.

Explanation:

The theorem used to interpret is:

If the chords of a circle that subtend equal angles at the centre, the end points of the chords are concylic
If two opposite angles of a quadrilateral add up to \(180^°\), then the vertices of the quadrilateral lie on a circle, i.e., they are concyclic.
The angles in the same arc segment are all equal.
If a line segment \(AB\) joining two points \(A\), \(B\) subtends equal angles at two other points \(C\), \(D\) that lie on the same side of \(AB\), then the four points lie on a circle.

The given points \(A\), \(B\), \(C\) and \(D\) are

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3. Concyclicity of points

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